Question

Write an equation for a polynomial with all the following features: The degree is 5, the polynomial has 4 terms and the graph of the polynomial crosses the vertical axis at y=12

Answer 1

we must apply the formula

`y=x^2+bx* c`
`3.25x^5+4x^{4^{}}\text{ }+5.5x^{3\text{ }}+x^2`

now we apply the formula to find x,

`\begin{gathered} h=(b)/(2(a)) \\ h=(-4)/(2(1)) \\ h=-2 \end{gathered}`

having already x now we apply the formula to find the vertex at y that intersects at point 12.

`\begin{gathered} f(-2)=3.25(-2)^{5\text{ }}+4(-2)^{4^{}}+5.5(-2)^{3^{}}\text{ }+(-2)^{2^{}} \\ f(-2)=104-64-44-8 \\ =-12 \end{gathered}`